ABSTRACT

Stretches of relaxed cat and rat muscle elicit similar history-dependent muscle spindle Ia firing rates that resemble history-dependent forces seen in single activated muscle fibers (
Nichols and Cope, 2004). Owing to thixotropy, whole musculotendon forces and muscle spindle firing rates are history dependent during stretch of relaxed cat muscle, where both muscle force and muscle spindle firing rates are elevated in the first stretch in a series of stretch–shorten cycles (
Blum et al., 2017). By contrast, rat musculotendon exhibits only mild thixotropy, such that the measured forces when stretched cannot explain history-dependent muscle spindle firing rates in the same way (
Haftel et al., 2004). We hypothesized that history-dependent muscle spindle firing rates elicited in stretch of relaxed rat muscle mirror history-dependent muscle fiber forces, which are masked at the level of whole musculotendon force by extracellular tissue force. We removed estimated extracellular tissue force contributions from recorded musculotendon force using an exponentially elastic tissue model. We then showed that the remaining estimated muscle fiber force resembles history-dependent muscle spindle firing rates recorded simultaneously. These forces also resemble history-dependent forces recorded in stretch of single activated fibers that are attributed to muscle cross-bridge mechanisms (
Campbell and Moss, 2000). Our results suggest that history-dependent muscle spindle firing in both rats and cats arise from history-dependent forces owing to thixotropy in muscle fibers.

In anesthetized cats, history-dependent spindle firing rates mirror history-dependent whole musculotendon forces during muscle stretch owing to thixotropy (Campbell and Moss, 2000). In muscles, thixitropy refers to the dependence of muscle force during stretch based on prior movement; thixitropy manifests as an elevated eccentric force when the muscle is stretched after it is held at rest versus after it is moving. We previously showed that thixotropy evident in whole cat musculotendon force and yank, i.e. the first time-derivative of force (D. C. Lin, C. P. McGowan, L. H. Ting and K. P. Blum, unpublished), precisely reproduces the fine temporal details of history-dependent firing of Ia afferents in a series of stretch–shorten cycles (Blum et al., 2017).

Here, we hypothesized that thixotropy in muscle fibers is masked by ECM forces throughout the muscle when examining whole musculotendon force during muscle stretch in anesthetized rats. We further hypothesized that muscle fiber forces, consisting of both contractile (e.g. actin–myosin forces) and noncontractile components (e.g. titin), in rats exhibit similar history dependence as muscle spindle Ia firing rates recorded simultaneously. We made the simplifying assumption that ECM and muscle fiber forces act in parallel, contributing additively to musculotendon force. ECM forces were estimated using a simple exponential–linear tissue model, and muscle fiber force was estimated by analytically removing ECM force from recorded musculotendon force. We found that a large proportion of musculotendon force was carried by the estimated ECM. Our data indicate that the muscle fibers are thixotropic, as the estimated muscle fiber force and its first time derivative, yank (D. C. Lin, C. P. McGowan, L. H. Ting and K. P. Blum, unpublished), were history dependent and closely resembled history-dependent muscle spindle firing rates recorded simultaneously. Our work suggests that history-dependent spindle firing and muscle fiber forces in rats and cats arise from thixotropy in muscle fibers.

MATERIALS AND METHODS

Animal care

All procedures and experiments were approved by the Georgia Institute of Technology's Institutional Animal Care and Use Committee. Adult female Wistar rats [Rattus norvegicus domestica (Berkenhout 1769); N=5; 250–300 g] were studied in terminal experiments only and were not subject to any other experimental procedures. All animals were housed in clean cages and provided food and water ad libitum in a temperature- and light-controlled environment in Georgia Institute of Technology's Animal Facility.

Terminal physiological experiments

Experiments were designed to measure the firing of individual muscle afferents in response to muscle stretch in vivo using electrophysiological techniques as documented previously (Vincent et al., 2017). Rats were deeply anesthetized (complete absence of withdrawal reflex) by inhalation of isoflurane, initially in an induction chamber (5% in 100% O2) and, for the remainder of the experiment, via a tracheal cannula (1.5–2.5% in 100% O2).

The triceps–surae muscle group in the left hindlimb was dissected free of the surrounding tissue and detached at its insertion together with a piece of calcaneus bone. The severed insertion of the left triceps–surae muscle group was securely attached directly to the lever arm of a force- and length-sensing servomotor (model 305B-LR, Aurora Scientific Inc.), to control muscle stretch while recording muscle length and force (dual-mode lever arm system, Aurora Scientific). Initial muscle tension was set to 0.1 N, the approximate passive tension observed for ankle and knee angles of 90 and 120 deg, respectively.

Firing rates and patterns of Ia afferents were studied in response to length-servo controlled stretches applied to triceps surae muscles at rest. Ramp–release stretches at constant velocity (4 mm s−1) were applied with amplitudes ranging from 0.5 to 3 mm. Trials of three to five sequences were repeated in between rest periods of at least 10 s allowing expression of history-dependent firing responses (Fig. 1B; Haftel et al., 2004). Musculotendon force, length and Ia-afferent action potentials were simultaneously recorded at a minimum of 20 kHz and down-sampled to at least 1 kHz for analysis. Yank was calculated as the time-derivative of recorded force (D. C. Lin, C. P. McGowan, L. H. Ting and K. P. Blum, unpublished).

Methods for recording muscle spindle firing rates and estimating muscle fiber force during stretch of relaxed rat muscle. (A) Intra-axonal recording from muscle spindle Ia afferents from dorsal rootlet were recorded during stretch of the triceps surae musculotendon. Muscle length (L) and total musculotendon force (F; panel on right) were recorded with membrane potentials; instantaneous firing rates (IFRs) were computed based on action potential events (traces in center panel). (B) Sets of identical triangular stretches were imposed at three lengths (1, 2 and 3 mm). Action potentials (gray lines) with superimposed instantaneous firing rate (black dots) are shown temporally aligned with simultaneously recorded muscle force, yank and length traces. In each trial, muscle spindle Ia firing response to identical stretch stimuli different in the first stretch when compared with subsequent stretches. Specifically, the response to the first stretch contains an initial burst of spikes at stretch onset and more pronounced dynamic response post-initial burst. (C) The recorded musculotendon force (FMT) was assumed to comprise two additive force components: one component arising from non-contractile tissues (Fnc; green) with an elastic force–length relationship and another component arising from the muscle fibers (Ffiber; red) with a series elastic component (black). (D) Musculotendon force (black) and yank (cyan) are overlaid to show similar exponential rise with imposed stretch (above). This suggests that a large component of the recorded musculotendon force arises due to an exponential elastic force. (E) Subtracting the estimated non-contractile force component (green) from the recorded musculotendon force (black) yielded the estimated muscle fiber force (red) and yank (blue), both of which were history dependent, with a larger response during the first stretch.

Muscle fiber force estimation

To isolate the muscle fiber force component, we assumed ECM was mechanically arranged in parallel to muscle fibers (Fig. 1C). We modeled ECM as elastic with both exponential and linear stiffness (Fig. 1D; Gillies and Lieber, 2011):(1)

where Fnc is non-contractile force, L is the entire musculotendon length, L0 is the musculotendon initial length, and klin is a constant for the linear element, and A and kexp are constants for the exponential element. ECM forces were subtracted from the recorded force to estimate the muscle fiber force, which resembled muscle spindle instantaneous firing rates (IFRs) (Fig. 1E). For each muscle (N=5), klin, A and kexp were initialized to values of 0.5 and optimized such that resulting estimated muscle fiber force (Ffiber), when multiplied by a constant, could explain the maximum amount of variance of the recorded Ia afferent IFR during 2 or 3 mm stretch trials (Blum et al., 2017). Parameters from one stretch in each animal was then applied in all other stretches of that muscle.

Variance accounted for of musculotendon force by estimated ECM force

We estimated the contribution of ECM to recorded musculotendon force at each perturbation length for a muscle using variance accounted for (VAF), defined as:(2)where the numerator represents the sum of squares of the ECM model for a given trial and the denominator is the total sum of squares of the recorded musculotendon force for the same trial.

where kF and kY are constant weights on fiber force and yank, respectively; bF and bY are constant offsets on fiber force and yank, respectively; and C is a constant. For visualization, we chose these parameters to be kF=1393 spikes Ns−1, kY=3.6 spikes N−1, bF=10 N, bY=5 N s−1 and C=34 spikes s−1. The yank and force components were subjected to a force threshold to emulate the spiking threshold of the neuron.

Statistics

Mean and standard deviation of ECM model parameters klin, A and kexp were calculated across animals (N=5). Mean VAF was calculated for each stretch length across animals to approximate the contribution of ECM forces to the recorded musculotendon force. First, the mean VAF across trials for each stretch length (0.5, 1.0, 2.0 and 3.0 mm) and each animal (N=5) was calculated (note: trials from at least three animals were used for each stretch length except 0.5 mm, for which we only collected data from one animal). Then, the means±s.e.m. of these values were calculated across animals, resulting in a single mean±s.e.m. VAF range for each stretch length (four ranges total).

RESULTS AND DISCUSSION

Rat muscle spindle Ia afferents exhibited history-dependent firing rates in response to repeated ramp–release stretches (Haftel et al., 2004). Initial bursts at the onset of the first stretch, and elevated firing rates during the first ramp were observed (Fig. 1B). In contrast, simultaneously recorded musculotendon force did not appear to be history dependent, apart from a small rise at stretch onset visible as a brief peak in yank (Fig. 1B). We observed an exponentially increasing force with stretch length (Fig. 1C).

ECM force contributions to whole musculotendon force increased with stretch length (Fig. 1D). Both the whole musculotendon force and yank signal exhibited a similar nonlinear rise with applied length – a property of an exponential relationship (Fig. 1D). The ECM component was thus modeled by linear and exponential parameters of klin=0.0497±0.0388, A=0.0454±0.317 and klin=1.071±0.362 (mean±s.d.; N=5 muscles). Using a single set of parameters for each muscle, the estimated ECM component accounted for 53±3% (mean±s.e.m.) of the total variance in force for 3 mm stretches, 34±3% for 2 mm stretches, 12±1% for 1 mm stretches and only 3% (data from one muscle) for 0.5 mm stretches.

Muscle thixotropy was reflected in the remaining signal representing the force in the muscle fibers and their series elements over time (Fig. 1E). This fiber force had a pronounced initial force rise and larger initial peak in the first stretch (Fig. 1E). This was accompanied by a larger peak in yank (Fig. 1E). Additionally, this rapid force increased, resulting in a higher overall level of force during the first ramp stretch compared with subsequent stretches (Fig. 1E).

The history dependence of muscle spindle firing rates, whole musculotendon force and yank, and estimated muscle fiber force and yank are illustrated by differences in the first stretch response versus subsequent responses (Fig. 2A). Muscle spindle firing rates were dramatically different on the first stretch relative to those on subsequent stretches (Fig. 2B, compare yellow with other colored traces). However, total musculotendon force and yank were quite similar across all stretches with only small differences between the first and subsequent stretches (Fig. 2C). Similarly, the estimated muscle fiber force and yank were clearly differentiated on the first ramp–release stretch (Fig. 2D). However, neither muscle fiber force nor yank individually resembled the history dependence of the spindle firing rates.

History dependence of muscle spindle firing rates, musculotendon force and yank, and muscle fiber force and yank. (A) Applied length depicted as time series (left panel). Different colors represent different stages of the perturbation. (B) Recorded firing rate from Ia afferent to applied length from A. Represented as time series (left) and as a function of length (right). (C) Recorded musculotendon force (top) and yank (bottom). (D) Estimated muscle fiber force (top) and yank (bottom) estimated from musculotendon force in C.

History dependence seen in muscle spindle firing rates (Fig. 3A,B) resembled linear combinations of muscle fiber force and yank, subject to a threshold (Fig. 3C,D). Although muscle spindle firing rates in 0.5 mm stretches (e.g. Fig. 3B) were qualitatively different than 2 mm stretches (Fig. 3A), they were still similar to the linear combinations of the estimated muscle fiber force and yank (Fig. 3C,D). These estimates were generated using the same weighting of force and yank at both stretch lengths (Fig. 3E,F). This robustness is all the more remarkable because the same ECM properties were used to estimate muscle fiber force and yank (Fig. 3G,H) at different stretch lengths where the amplitude of the ECM forces differed dramatically (30.2% versus 3.1% VAF of the total musculotendon force, respectively, for 2 and 0.5 mm stretches). In particular, the flatter muscle spindle response during the first ramp–release (Fig. 3B, yellow trace) was also present in the linear combination of muscle fiber force and yank (Fig. 3D, yellow trace).

History-dependent muscle spindle firing rates at different applied lengths resembled linear combinations of muscle fiber force and yank subject to a threshold. Muscle spindle firing rate for the afferent in (A) 2 mm and (B) 0.5 mm stretches. (C,D) Linear combination of estimated muscle fiber force and yank subject to a threshold exhibited the same qualitative features in both stretch conditions (a.u., arbitrary units). (E,F) The same weights (and offsets, not shown in diagram) were used in both stretch amplitudes to combine (G,H) estimated muscle fiber force and yank signals. kF, constant weight on fiber force; kY, constant weight on yank.

In summary, history-dependent muscle fiber forces during stretch of relaxed rat muscle can be identified from whole musculotendon force even when the majority of that force arises from stretch of ECM. ECM force dominated the musculotendon force and yank traces, consistent with reports that muscle fibers carry as little as 15% of total musculotendon loads in rodents (Meyer and Lieber, 2011, 2018). The remaining residual force was a relatively small component of the total force but resembled characteristics of isolated, activated muscle fibers in ramp–release stretches (Campbell and Lakie, 1998; Campbell and Moss, 2000, 2002), with an initial short-range stiffness (Getz et al., 1998), as well as higher mean force during the first ramp stretch.

The estimated muscle fiber forces exhibited thixotropic characteristics that were similar to history dependence in muscle spindle afferents recorded simultaneously, suggesting similar muscle force mechanisms in both cats and rats. The thixotropy we studied has been suggested to arise from muscle cross-bridge attachments and only occurs in the presence of Ca2+ (Campbell and Moss, 2002), although activation-dependent titin stiffness has also been suggested as a potential mechanism (Labeit et al., 2003). It appears that these well-known thixotropic properties of muscle fibers dominate history dependence in musculotendon force, and considering thixotropic properties of ECM (Barbenel et al., 1973) would not qualitatively alter our interpretations. The firing rate of muscle spindle primary afferents is directly related to the intrafusal muscle fibers of the spindle, with only a small amount of connective tissue force contributing to spike generation (Banks et al., 1997; Boyd et al., 1977). In relaxed muscle, we assume that the intrafusal and extrafusal muscle force exhibit similar responses to stretch; thus, we used the estimate of muscle fiber force as a proxy for intrafusal force. Our work shows that history dependence in both rat and cat muscle spindles arises from thixotropic effects on muscle fiber force when stretched. Although the results demonstrated in this paper support our hypothesis, more comprehensive studies should be performed to more quantitatively describe this mechanism.

Our study further provides a neuromuscular explanation for the tendency of human subjects to underestimate forces at longer musculotendon lengths owing to the stretch of ECM. Psychophysical studies demonstrate that human participants tend to only perceive forces generated by muscle fibers, and not passive components of force (Tsay et al., 2014). This sense of ‘fiber-only’ force is consistent with the finding in the present study that muscle spindles only fire in response to the force in muscle fibers, but not in ECM. Although Golgi tendon organs also sense active muscle force, they are located in-series with both muscle fibers and ECM and are unable to differentiate contractile and non-contractile force. The high contribution of non-contractile forces to whole musculotendon force during muscle stretch in rats could also explain the fact that Golgi tendon organ Ib afferents fire robustly to stretch in rats, but not cats (Vincent et al., 2017).

Taken together, our results suggests that muscle spindle firing rate reflects muscle fiber forces during passive stretch across different species. The dissociation of the encoding of muscle fiber and ECM forces may be important in understanding the role of proprioceptors in sensorimotor control, and the similarities and differences across species (Vincent et al., 2017). Differences in prior experiments between cats and rats may simply be due to differences in the relative amplitude of stretches, as larger stretches in cat muscle do engage ECM, which has an exponential characteristic (Gillies and Lieber, 2011; Matthews, 1933) and would likely need to be considered for larger stretch amplitudes. Indeed, when homologous muscles in the cat, rat and mouse are stretched with similar strain, firing responses of Ia afferents in each species are similar despite differences in the shape of musculotendon force (Carrasco et al., 2017). Further, in our anesthetized conditions, intrafusal forces within the muscle spindle encoding region is assumed to be similar to the extrafusal muscle force; we speculate that this assumption would also hold when a muscle and spindle are under beta control or alpha-gamma coactivation (Edin and Vallbo, 1990; Prochazka and Gorassini, 1998), but not when gamma motor drive differs significantly from alpha motor drive. We hypothesize the fundamental idea that muscle spindles fire in response to intrafusal muscle force and yank is generalizable across both passive and active movement conditions, reinforcing the necessity of considering intrafusal muscle state when examining muscle spindle function.

Acknowledgements

We thank David Lin for introducing us to the term ‘yank’ as the first time derivative of force.

This work was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development [R01 HD90642 to L.H.T. and T.C.C.], the National Institute of Neurological Disorders and Stroke [P01 NS057228 to T.C.C.] and the National Institute of Neurological Disorders and Stroke [F31 NS093855 to K.P.B.]. Deposited in PMC for release after 12 months.

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